To find the inverse of the function \( f(x) = 2x - 10 \), we will follow these steps:
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Replace \( f(x) \) with \( y \): \[ y = 2x - 10 \]
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Solve for \( x \) in terms of \( y \): \[ y + 10 = 2x \] \[ x = \frac{y + 10}{2} \]
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Now, replace \( y \) with \( x \) to express the inverse function: \[ f^{-1}(x) = \frac{x + 10}{2} \]
Now let's check which of the given options matches this result.
The options were:
- \( h(x) = 2x - 5 \)
- \( h(x) = 2x + 5 \)
- \( h(x) = x - 5 \)
- \( h(x) = x + 5 \)
None of these options match the derived inverse function \( f^{-1}(x) = \frac{x + 10}{2} \), which simplifies to \( h(x) = \frac{1}{2}x + 5 \) when you distribute.
Thus, none of the provided options are correct. The correct inverse of \( f(x) = 2x - 10 \) is \( f^{-1}(x) = \frac{x + 10}{2} \).